Model selection for spatiotemporal modeling of early childhood sub-cortical development

Spatiotemporal shape models capture the dynamics of shape change over time and are an essential tool for monitoring and measuring anatomical growth or degeneration. In this paper we evaluate non-parametric shape regression on the challenging problem of modeling early childhood sub-cortical development starting from birth. Due to the flexibility of the model, it can be challenging to choose parameters which lead to a good model fit yet does not overfit. We systematically test a variety of parameter settings to evaluate model fit as well as the sensitivity of the method to specific parameters, and we explore the impact of missing data on model estimation

Crater population and resurfacing of the Martian north polar layered deposits

Present-day accumulation in the north polar layered deposits (NPLD) is thought to occur via deposition on the north polar residual cap. Understanding current mass balance in relation to current climate would provide insight into the climatic record of the NPLD. To constrain processes and rates of NPLD resurfacing, a search for craters was conducted using images from the Mars Reconnaissance Orbiter Context Camera. One hundred thirty craters have been identified on the NPLD, 95 of which are located within a region defined to represent recent accumulation. High Resolution Imaging Science Experiment images of craters in this region reveal a morphological sequence of crater degradation that provides a qualitative understanding of processes involved in crater removal. A classification system for these craters was developed based on the amount of apparent degradation and infilling and where possible depth/diameter ratios were determined. The temporal and spatial distribution of crater degradation is interpreted to be close to uniform. Through comparison of the size-frequency distribution of these craters with the expected production function, the craters are interpreted to be an equilibrium population with a crater of diameter D meters having a lifetime of ~30.75D^(1.14) years. Accumulation rates within these craters are estimated at 7.2D^(−0.14) mm/yr, which corresponds to values of ~3–4 mm/yr and are much higher than rates thought to apply to the surrounding flat terrain. The current crater population is estimated to have accumulated in the last ~20 kyr or less

Detailed stratigraphy and bed thickness of the Mars north and south polar layered deposits

The Mars polar layered deposits (PLD) likely hold an extensive record of recent climate during a period of high-amplitude orbit and obliquity cycles. Previous work has detected limited evidence for orbital signatures within PLD stratigraphy, but data from the High Resolution Imaging Science Experiment (HiRISE) permit renewed analysis of PLD stratigraphy at sub-meter scale. Topography derived from HiRISE images using stereogrammetry resolves beds previously detectable only as alternating light and dark bands in visible images. We utilize these data to measure the thickness of individual beds within the PLD, corrected for non-horizontal bed orientation. Stratigraphic columns and bed thickness profiles are presented for two sites within the NPLD, and show several sets of finely bedded units 1–2 m thick; isolated marker beds 3–4 m thick; and undifferentiated sections. Bed thickness measurements for three sites within the SPLD exhibit only one bed type based on albedo and morphology, and bed thicknesses have a larger mean and variance compared to measurements for the NPLD. Power spectra of brightness and slope derived along the measured stratigraphic sections confirm the regularity of NPLD fine bed thickness, and the lack of a dominant SPLD bed thickness. The regularity of fine bed thickness of the NPLD is consistent with quasiperiodic bed formation, albeit with unknown temporal period; the SPLD thickness measurements show no such regularity

Geodesic image regression with a sparse parameterization of diffeomorphisms

International audienceImage regression allows for time-discrete imaging data to be modeled continuously, and is a crucial tool for conducting statistical analysis on longitudinal images. Geodesic models are particularly well suited for statistical analysis, as image evolution is fully characterized by a baseline image and initial momenta. However, existing geodesic image regression models are parameterized by a large number of initial momenta, equal to the number of image voxels. In this paper, we present a sparse geodesic image regression framework which greatly reduces the number of model parameters. We combine a control point formulation of deformations with a L 1 penalty to select the most relevant subset of momenta. This way, the number of model parameters reflects the complexity of anatomical changes in time rather than the sampling of the image. We apply our method to both synthetic and real data and show that we can decrease the number of model parameters (from the number of voxels down to hundreds) with only minimal decrease in model accuracy. The reduction in model parameters has the potential to improve the power of ensuing statistical analysis, which faces the challenging problem of high dimensionality

Geodesic shape regression in the framework

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